1. Field of the Invention
The present invention is directed to the field of material analysis. In particular the field of the invention is directed to strain mapping of materials.
2. Description of the Related Technology
Measurement of strain in crystalline materials is of interest for several reasons. Local strain can have an effect on the properties and performance of materials, but also, it often serves as a driving force for microstructural evolution. Microstructural evolution is the change in the internal structure of the material, as in the positions of the atoms relative to one another, both in terms of their immediate neighbors and on a longer scale. Increased dislocation densities provide greater strength and hardness, but a decrease in ductility. Thermomechanical processes such as rolling and annealing rely on the stored energy from dislocations to act as the driving force for recovery and recrystallization. By controlling these processes, finely tuned microstructures can be produced to meet specific requirements. Quantifying dislocation densities is crucial to understanding deformation, recovery, and recrystallization and the specific mechanisms that drive them.
In analyzing the strain in materials, a number of techniques exist. A primary technique available for strain measurement on the nanoscale is geometric phase analysis (GPA). GPA is a post-imaging process for mapping of strain in a high resolution TEM (transmission electron microscope). GPA can achieve very accurate results at sub-nanometer resolution. GPA also allows for precise measurement of elastic strain that occurs independently or due to the distortion caused by defects introduced through plastic strain, i.e. dislocations. However, a drawback of GPA is that it requires that the high resolution TEM image being used was taken on a zone axis such that the lattice of the material is directly visible, and that there is a strain-free reference area contained within the image.
GPA may be used for mapping the strain around individual defects in an otherwise perfect crystal. For example the strain fields associated with the dislocations that make up a low angle grain boundary. This limits the usefulness of GPA with respect to polycrystalline materials and thicker specimens where such high resolution is not always attainable. Furthermore, it is difficult to capture a region that is truly free of strain to use for a reference, especially in the same frame as the defect that is targeted.
In addition to GPA, there are other small-scale strain mapping techniques available, such as various post analyses of scanning electron microscope (SEM), EBSD maps, holographic interferometry in TEM, or X-ray diffraction strain imaging.
Despite improvements in resolution, SEMs are limited to a minimum spatial resolution of approximately 40 nm. This drawback, along with its nature as a surface characterization technique, makes SEM less than ideal for measuring dislocations.
Dark-field holographic interferometry is an improvement on GPA because it is capable of capturing a larger field of view with a similar resolution as that of GPA. However, it is limited in terms of what samples it is applicable to; specifically, the sample must consist of a cross-section of unstrained substrate and a strained film such as that produced by molecular beam epitaxy. While this sample geometry may be found in microelectronic devices, it is not possible to achieve this geometry for bulk polycrystalline materials.
The primary drawback to strain imaging using X-ray diffraction (XRD) is that while it is possible to measure average strain with accuracy on a typical XRD instrument, in order to achieve a spatial resolution on a nanometer scale a synchrotron source must be used. Additionally, the resolutions achieved are not as high as those capable of being achieved with existing TEM strain mapping techniques.
There are a number of approaches to measuring the strain using EBSD. Strain in the crystal lattice leads to slight changes in the Kikuchi patterns. However these slight changes are difficult to detect, especially at the low resolutions used for rapid pattern acquisition over a large scan area. EBSD techniques are limited by the resolution of backscatter detectors and the relatively large step sizes used in EBSD scans. In recent experiments performed on copper bi-crystals, the best case lateral and longitudinal resolution for an EBSD scan was determined to be 34 by 45 nm.
Another method is described in the publication WO 2010/052289. This reference describes a method and device for electron diffraction tomography of a crystal sample which employs scanning of an electron beam over a plurality of discrete locations of the sample in combination with a beam scanning protocol, as the beam converges at each discrete location of the sample to obtain a series of electron diffraction patterns, use of template matching is performed to determine crystal orientations and thickness maps to in order to obtain a common intensity scaling factor. The disclosure of WO 2010/052289 is hereby incorporated by reference to the extent that it provides details of electron diffraction tomography and template matching.
While the above described methods for strain mapping are useful, there is still a need for improved methods of producing strain maps of materials.